Method of gutting geabs



- H. 0. WILLIAMS. METHOD 0F CUTTING GEARS.

l APPLICATION FILED DEC. Il 1917- 1,404,505.

Patented Jan. 24, 1922.

4 SHEETS-SHEET l.

H. D. WILLIAMS.

METHOD 0F CUTTING GEARS.

APPLICATION FlLEn DEc.11.1917.

Patented Jan. 24, 1922.

4 SHEETS-SHEET 2.

H. D. WILLIAMS.

METHOD 0F CUTTING GEARS.

APPLICATION FILED DEC.II,I9I1.

` 1,404,505, Param-.ed Jan. 24,1922.

4 SHEETS-SHEET 3. ,iz/@9 7.

8 Eff l H. D. WILLIAMS.

METHOD 0F CUTTING SEARS.

APPLICATION FILED DEC. II, |917.

1 ,404,505, Patented Jan. 24, 1922- 4 SHEETS-SHEET 4.

UNITED STATES lii'lliN'l' OFFICE.

HARVEY D. WILLIAMS, O'WALLNGEDRD, CONNECTCUT, ASSGNOR, BY MESNE ASSIGNMENTS, '10 SECUBETY TRUST CGMPANY, OF DETROIT, MCHGAN, A COR- FORATION OF MCI'IGAN.

METHOD DE OU'I'TING Specification of To all 'Lc/tom mog/ concern.'

Be it known that l, l-innvnr l). illuminare, a citizen of the United States, and resident oit l/Vallingford, New ilaven County, State or' Connecticut, have invented certain new and useful Improvements in Methods ot Cutting Gears, oit which the following is a specification.

This application relates to the method ot cutting' the gears described and claimed in my to-pending application. Serial No. 853,- 017, tiled July 25, i914, and renewed Deceniher 5, 191i', Serial No. Q-Oll, on which lietters Patent No. 1,32%,287 were issued Deeeinber 9, i919. The present application is division of said earlier application.

rlhis invention relates to that class oit toothed gearing in which the wheel ineinber of a pair oi' gears, has the teeth thereof angularly-disposed relatively to a line that is normal tothe plane of revolution or in other words parallel to the axis of revolution of such wheel.

In said pending application l have dcscrihed a system of toothed gearing in which a pair oi the gears comprises a wheel having the working surfaces ot its teeth conforming to a single-reproduction coi'iiiguration and a mating pinion having the working surfaces of its teeth conforming to coacting compound-reproduction configuration; thiis the teeth of the gear wheel and the teeth oi the mating pinion therefor are dissimilar' 'formation or configuration. lt is one ot' the objects of the present invention to urnish a method olf cutting such toothed gearing,

also in said pending application lave described gearing in which the proiiles-pairs (throughout the length oi the tooth surfaces of the wheel) are uniiiorin in relation to a geometri; master-torni axis and are also uniiiorin in relation to geometric plane in which said master-forni axis is located as therein inou fully explained. lt is one or the ohjects ot the present invention to turnish a niethod ci cutting such gearing.

Also, in said pending application l have described toothed gearing in which the longitudinal line or geometric axis ol' each pair of adjacent tooth surfaces is disposed or located in an angular relation to the axis of revolution as in certain kinds of bevel ersatent- Patented Jan. 24, 1922.

853,017. Patent No. 1,324,287, dated December 9, December 11, 191'?. Serial No. 206,583.

and shew-bevel and skew-spur gears; also such gearing in which the wheel ot a pair gears constitutes a master-wheel adapted ior operatinO correctly not only with pinions of varying diameters but also with such pinions located with their axes in various degrees of divergence or axial shew, respectively, from an axial-plane radial to the inaster-wheel axis and also relatively to the plane of rotation ot the wheel. lt is one ot the objects ot the present invention to turnish a method of cutting such gearing.

ln view of the intricate kineniatical relations involved in the art of toothed-gearing, and especially when the teeth. are angularlydisposed, as in the present iinproveinents, l have herein employed the terin wheel for designating` the gear having the teeth thereoiv provided with the working-faces having a singlereproduction coniiguration, and have designated the 'mating gear as the pinion, without regard, however, to their relative actual sizes but having in mind that usually the wheel is larger than the pinion, and that while either one may be used as the driver, the smaller said gear will preierably and usually be the pinion and be einployed the driving nieinber of the pair of gears7 ln iny improved toothed gearing above ree 'red to the wheel has working faces of a o ni adapted to be readily precisioned, and hese working surfaces are arranged in a longitudinal parallelism, and also in a transversely converging relation to each other. The generated or evolution forni of toothsurfaces is thus restricted to one gear (the pinion) of the pair, while the other gear, or wheel, has non-evolved teeth oi a shape and relative size which are niore readily producihle with the required high degree of precision, and which are producible and repairahle by the use of siinple and ordinary appliances and inethods and without requiring the use oi any generating machines for forming or shaping the tooth surfaces. Thus the present invention comprises a method of producing a pair ot bevel gears by cutting one oi said gears, as the wheel, by a single-reproduction relative nioifeinent between the wheel blank and the cutting edges oi a tool to thereby produce a pair of adjacent tooth surfaces which have parallel surface ele- CTI ments and which together constitute a master-form, and in cutting the other of said gears, as the pinion, by a compound-reproduction relative movement between the pinion blank and cutting edges which correspond to such master-form.

In the accompanying drawings which form a part of this specification, I have illustrated the novel form of gearing produced by the method forming the subject matter of this invention, and I have likewise indicated, somewhat diagrammatically, the various tool and blank movements which are gone through with in the cutting of these gears.

ln the drawings, Fig. 1 is a diagrammatic View illustrating (but in a general way only) certain relations of the wheel and pinion, and especially the relation of their respective tooth-surfaces with each other;

Fig. 2 is a fragmentary sectional view (drawn in alinement with Figs. 1 and 3, as indicated by the dotted line sti-fc, which in Fig. 1 passes through the master-form axis at rv) showing portions of a spur-wheel and pinion having teeth which are here shown in side view, and which correspond in construction with those indicated in end view in Fig. 1;

F ig. 3 is a similar fragmentary sectional view showing portions of a bevel wheel and pinion having teeth which are here shown in side view, and which c orrespond in construction with those indicated in end view in Fig. 1;

Fig. Q is a fragmentary view drawn below and in alinement with Fig. 2, and showing a portion of the spur-wheel B (Fig. 2), and in plan or face view, a pair of tooth-surfaces,

f3, f5, arranged with a tooth-space between them and also located with an Obliquity indicated by the angle e6;

Fig. 3a is a similar fragmentary plan or face view of a portion of the bevel wheel B, (Fig. 3), showing a pair of the tooth-surfaces as f3, f5, arranged on the face or toothzone with the master-form axis a: located in a plane of the aXis-of-revolution, c, of the wheel;

Fig. 4 is a view similar to Fig. 3, but showing the pair of tooth-surfaces arranged on the tooth-zone or face, N, with an obliquity as indicated by the angle es;

Fig. 5 is a diagram drawn in a manner similar to a perspective view, for illustrating the geometrical relations of certain features of the wheel member of a pair of the gears, and for showing the master-formaxis in three arrangements or locations co inciding, respectively, with three locations of acertain hypothenuse line which is here shown in the successive positions fr, 0112, and and w13; Y

Figs. G and 6a are diagrams for illustrating certain features hereinafter more fully explained, regarding the outward and the inward arrangements of the convergence of. the tooth surfaces;

Figs; 7, 8 and 9 are diagrammatic views illustrative of the preferred method of male ing the gears when the wheel B (in a conical form thereof) has the master-form planes inwardlyconverging Figs. 10 and 11 are views similar to Figs.7 and 9, respectively, for similarly illustrating the method when applied to the making of gears in which the said master-form planes are outwardly-converging.

Figs. 12, 13 and 14 are views similar to Figs. 7, 10 and 8, respectively, for illustrating the counter-part tools J and T for making pairs of tooth-surfaces in skew-spur wheels by the method of single-reproduction, and when the master-form axis m is in the position x13, Fig. 5;

Fig. 15 is an oblique view for more fully and clearly exhibiting the features indicated in Figs. 12, 13 and 14;

Fig. 16 is a view similar to Fig. 9, for illustrating the manner of applying the master-form tool T (Figs. 12 and 1B) for making pairs of generated tooth-surfaces on the skew-spur pinion by the method of compound-reproduction, and for mating with a skew-spur wheel such as indicated in Figs. 1, Q, 2, and in Figs. 12, 14, 15;

Fig. 1Gn is a view drawn in alinement with Fig. 16 showing the skew-spur pinion, seen from the left hand in Fig. 16) g and Fig. 1Gb is a view of the said pinion as seen from above in Fig. 16a.

ln a pair of intermeshing gears, and as between the'body of a wheel-tooth and the body of a pinion-tooth, the proper rolling movement. requires, in any given instance, some aggregate amount of transverse-curvature, or profile deviation, of the one toothsurface relatively to the other, and in the former practice it was customary to apportion that total relative curvature one part to the wheel and the remaining part to the pinion and to make a` different apportionment for each pair of gears having different relative diameters. ln this system of gearing, and contrary to that former practice, no such separate apportienments are required, but the whole of such relative deviation may be applied to the pinion-tooth surfaces. This feature combined with the longitudinal-parallelism of the pairs of wheel toothsurfaces, and with these surfaces transversely converging, is a means for bringing the two said members of the pair of gears into such a relationship that in addition to having the improved operational features herein set forth, the wheel teeth can be made on a series of wheels by the single-reproduction method and with the same master-form and the same counterpart tool, while only the pinions require the compound-reproduction method for their manufacture.

In a pair orp mating gears for operating in only one direction, each o1E the coacting teeth need have, as is Well known, only one Working-surface, but these working-surfaces, in the gearing herein described, are or' the singlereproduction arrangement and coniiguration on the Wheel-teeth and have uniform profiles throughout their length, While the coacting tooth-surfaces on the pinion teeth are conjugate to said Wheel-tooth 'Working-surfaces and are of the compoundreproduction arrangement and configuration. Each Wheel-tooth Working-surface has uniform profiles throughout the length thereof and is of the single-reproduction contieuration, but When each ot said teeth has tivo such Working-surfaces, and has these arranged in such relation that a pair oit them (either tivo surfaces on one tooth or two surfaces on each oi' tivo adjacent teeth), are formed in parallel, such pair of working-surfaces is said to conform to the single-reproduction arrangement and configuration; and, conversely, the coacting piniontooth Working-surfaces Will then be :formed in pairs which are said to conform to the compound-reproduction arrangement and configuration. lVhen thus organized, each pinion-tooth is provided with a pair of Working-surfaces which are individually conjugate to the respective Working-surfaces of said Wheeltooth pairs, and which also, when taken as, or in pairs, contorni to the compound-reproduction arrangement and coniiguration. In these arrangements, the Wheel-tooth Working-surfaces are, of course, transversely-converging,7 either outwardly, as in F ig. 6a, or inwardly, as in Fig. 6.

In this system of oblique toothed gearing, the pinion has the Working-surfaces of its teeth, (Which are sometimes herein also designated as tooth-faces, and as tooth-surfaces) shaped according to a compound reproduction, which may be effected, as hereinafter set torta-by' means oi the counterpart tool having a movement parallel to the obliquely-located axis, as a; (see Figs 8, 9) oi the master-form, as F, oi the Wheel, and also having concurrently with and relatively to the pinion, a rolling movement in accordance with the geometric pitchsurfaces.

Usually the larger gear, as B, Fig. 2, of a pair oi these oblique gears is properly regarded as being the ivheet This Wheel member is provided With obliquely-disposed teeth which have their workingsurtaces arranged in transversely converging pairs in which each of said tooth-surfaces has a unitorni proiile throughout the length thereof. These tooth-surfaces are also arranged. in pairs which are longitudinally parallel the one to the other, so that in any such pair ot tooth-surfaces their normal operation involves a peculiar progressively meshing action as between the Wheel tooth-iaces and the faces oi: a co-meshing pinion. This peculiar meshing action,-ior the salie of brev- .ity and tor the Want ot a better term,-l

have designated as a shew-action. ln this gearing', therefore, there is a certain skewaction ot the tooth-faces which is normal to the operation of the gears, and which involves a relatively progressive meshing, longitudinally oi the teeth during the approach into full-inesln-so that some variation in the skew angles does not, in etiect, create a different hind oi' coaction, although. varying the same in both a qualitative and quantitative manner. Thus a slewaction involving a longitudinally progressive meshing, as between the working-surfaces oit the obliqiiely-clisposed wheel-teeth and the coacting but diilerently shaped surfaces or the pinion teeth, is obtained with pinions of diierent sizes and having respectively,

.dii'lerent skew or angular locations oit the pinion-axis relatively to the Wheel-axis.

The aforesaid directly-coacting faces being arranged in converging pairs, and these pairs, as f3, f5, Fig. 5 and f3, f5, Fig. 6, be ing alike except as to the direction oi the convergence (here shovvn by arrows), each such pair of the converging faces constitutes a structural feature which l designate as the master-torni. 'A iiurther feature oi this cmastentorrn is the longitudinal parallelisin of the s, l tivo transverselyconverging tooth-surfaces which are comprised therein, and the similar parallelism or the surface-element lines of such tooth-surfaces relatively7 to a geometric "inastentorni-axis, as au ln some of the views the masteniorin is shown applied to the Wheel-tooth, which thus has paralle faces, While in other viewsr the inasteri'orni is shown applied to `'the tooth-spaces, as F, the Wheel-tooth surfaces, as j, fr-being shown offset in parallel troni the inaster-form-axis ln a pair of these gears, when the Wheel has the master-form with its center-line, as ai, (see Fig. 3a) in the position m, 5, Where said center-line is shown located in plane radial to the Wheel axis, the tivo tooth-surfaces, as f3, f5 (see Fig. have a shew-angle, cl3, relation to said Wheel-axis, one ot them, as f3, has a rearward slrevf. Similarly, the pinion P has its tooth-surfaces arranged ivith their bounding mastertorin surfaces, and hence their suriiace elements in general,-located on similar skewangles, and these in relatively the saine order ci arrangement. Vifhenthe action-tace, as fi", oi' the Wheel has a rearward slreiv, (see Fig. 3a), the amount of which is indicated by tie angle @13, the enacting pinion tootlr surface Will have a corresponding amount oi' shew in the said direction. ln this pinion construction, therefore, the masterforni of or for the pinion tooth-surfaces has the two sides 'thereof in longitudinal parallelism, in this respect corresponding with the wheel construction. Then the wheel master-form has the inwardly-converging longitudinally parallel surfaces (and therefore has the parallel spaces, as F) the pinion master-form has, relatively to the pinion pitch-surface, the outvvardly-converging arrangement of the said master-form bounding,` surfaces or tooth faces. Therefore, these two master-forms come into the same positions and coincide when the two engaging' tooth-sections also come to the exact fullmesh position.

In each of the described arrangements of the convergence of the said wheel tooth-surfaces, these wheel-tooth surfaces, (in any series of the master-forms having the longitudinally parallel construction), are so arranged and related that, as shown in Fig. et, in any group of three successive wheel tooth faces, two of these are arranged in parallelism with each other, and since in practice at least three successive wheel-tooth faces will be in mesh to the extent of having a full working` engagement, therefore at all times in such a set of three successive faces there is a direct parallel (dir ctly opposite) action and re-action, respectively, upon a pair of longitudinally-parallel faces which are one of them next succeeding to the other of them in the circumferential tooth-zone N of the wheel. rthis peculiar relationship and mode of coaction, is indicated in Figs. 3 and et, and other views, and particularly in said Fig. 3a, where the two inwardlyconverging successive faces 2l and Q2 are in parallel, while the next successive face, 23, is at an angle, as l2, thereto. Also in said Fig. 8, another set of three successive faces comprises the two outwardly-converging longitudinally non-parallel faces 22, 23, and the next succeedingl parallelly-disposed face 2441. ln each of these two sets of groups, the directly opposite action and reaction is indicated by the parallelism of the two oppositely-acting` faces, as 2l, 22, in the one and 2B, Qfl in the other set.

Referring to the diagram Fig. 5, if a line, as 2a, which is normal to the axis at the point c, be rotated about said axis, the outer end of said line 2a describes the meridian circle mi", located in a plane of rotation. At some other point, as c', on said axis m3, describe a similar circle as m4, also in a plane of rotation; the two circles then lie in parallel planes, and these planes are at rightangles to the axial line 503, which represents the axis of rotation of any gear or wheel that shall be drawn out or designed in accordance with the diagram thus arranged or proportioned. ln practice, as will be evident, the diagram, Fig. 5, may be made of such proportions as are suitable for meeting the requirement-s in any given pair of gears to be made in accordance with my presentimprovements. lt will be seen that the circle m5 is an orbital path in which the point e may be said to revolve around the point y of the circle m". Said orbital circle fmf" is shown divided by the lines 3a, 3b, into arcs, of which the quadrant c to .a is the lower right-hand quadrant, extending in the circle m5 from the line at the point c', to the line m13, at the point e, these lines a1 and w13 being diderent positions of a hypothenuse line.

lThe said hypothenuse line, as m13, at the vertex of the triangle me, y, e F ig. 5, intei-sects or contacts with the instant axis, m, and this is in a plane of rotation which, for convenience, l designate as the meridian plane, and in which lies the circle m3; this plane is also the profile meridian. When the described locating-triangle mi, y, e, Fin'. 5, has the plane thereof, (which is indicated by the line y, a) located in a tangential relation to the meridian-circle m3, and also tangential to the geometrie surfac'e-of-rei" lution generated by the instant axis m revolvingv about the wheel-axis m, and the tooth-Zone of the wheel, as N", Fing. Qa, heing located contiguous to said meridian-circle m3, the gear-wheel (ses Fig'. is then of the particular kind which l designate as skew-spur gearing.

In a pair of these gears, when the wheel has the master-form with its center-line, as rc, Fig. 5, in the position (which is also in a plane radial to the wheel axis) the two tooth-surfaces, as and (see Fig. 3a) have a skew-angle relation to said wheelaxis, one of them, as f5, having a forward skew while the other said face, as f3, has relatively a rearward skew. Similarly, the pinion l) has its tooth-surfaces arranged with their bounding,` master-form surfaces, and hence their surface elements in general, located on similar skew-angles, and these in relatively the saine order of arrangement. 1lllhen the action-fa ce, f5, of the wheel has a rearward shew, the amount of which indicated by the angle 013, the enacting pinion tooth-surface' will have a correspondingl amountl of skew in the said direction. ln this pinion construction, therefore, the masterorm of the pinion tooth-surfaces has the two sides thereof in longitudinal parallelism, in this respect corresponding` with the wheel construction. l3nt when the 'wheel masterform has the inwa-rdly-converging longitudinally parallel surfaces, (and therefore has the parallel, spaces), as F (Fig: l) the pinion master-form has, relatively to the pinion pitch-surface. the outwardly-converging arrangement of the said master-forni7 bounding-surfaces or tooth-faces. Therefore these two master-forms come into the same positions and coincide when the two engaging tooth-sections also come to the exact fullmesh position, this being illustrated at fr, Fig. l.

From the foregoing description as herein illustrated, it will now be evident how thc master-torm-axis is not only a line located in a plane, but also is a line having an angular position relatively to the Wheel-axis, to the plane of rotation and to any straightline that is a normal to (perpendicular Jto) such plane of rotation; and how, in the pinion the corresponding tootlrsuritme axial lines, of the respective toothnsuriace pairs, are rotational trace-lines of said Wheel master iorm axis,

lin practice, any desired number oi' changeable pinions of different sizes respectively, may have their working-surfaces shaped by the method compound-repro duction, or evolution, trom and by the counterpart or the same master-form F, by generating the pinion teeth from a rolling movement on the geometric pitch-surfaces. ln this operation pitch-surfaces resulting from the rolling movement will, of course, meet on an axial line, as :0, Figs. 9 and i6. in any such case. however, the samecounterpart tool, as T, having a profile outline coinciding with said master-form (or a suitable correspondingly-shaped milling-cutteii, -not shown, in lieu thereof), will properiy generate the corresponding pinion-tooth curved-surface of the conjugate torni tor Working correctly upon the tooth-surfaces of such master-Wheel. rlhus a single masten Wheel may constitute a master or form for generating the teeth on any plurality' ot pinions oi" dilierent sizes, respectively, and each specially shaped ioi rolling correctly in mesh with that one muste1-\vlieel; but `these diii'eu ent pinions, being each thus specially shaped, are not thereby formed for Working in i..esh with each other, nor with a master-Wheel oi a dilierent size or proportion. in all such instances, however, the pinion toothsuriiace may be properly described as having a developed curvature generated Caccor/cling to"7 the tooth-suriaces the mating Wheel oi the pair. These pini laces are said. to be generated because in. practce they will be, usually and preferably, produced in and by some suitable r-tootliw generating machine. the tootlrsuri'atc., beine,- developed irorn and by tool `whose cut lines are made according to the torni oi the master wheelpairs ot tooth that the resultant or c apigate "i transverse curvature will be oi the same ideveloped7 formation as it the tooth 'laces ot the pinion were actually moulded into shape by the rolling oi? the pinion in mesh with its oivn masternvheel.

l Will nov.Y briefly explain one method oi' making the master-form surfaces ci the Wheel, tiretreiterring to conical Wheels having obliquely-disposed tooth-surfaces), and the use ci the counterpart tools `lor making the conjugationally-curved pinion-tooth surlaces by the duplicate oi the master-form of the Wheel with which such pinion is to mesh.

In Fig. 7 the ellipse 8 is lthe outer circle of the Wheel B, the line of sight being parallel to the axis a of the centrally located master-form at F; this view also shows the Woilingsuriaces ot said master-form arranged .inwardly-converging. ln Fig. S a section is shown of the tooth-rim ci -the Wheel B, as seen from the right-hand in Fig. 7, the tooth-surface f3 being shown fully formed, While the master-form axis x indi- Cates, also, the line ot' movement of the tool J, the profile-outline oi which (Fig. 7) should correspond with some selected master-form F, for the Wheel B. rlhe Wheelblanlr being properly held in a Well-known manner in a suitable inoexing-shaping machine (not shown), and the tool J being reeiprocated While carried in the usual toolholder of such Well lnovvn shaping machine the tool may then be ted gradually downward to its said position in Figs. T and 8, ythereby reproducing the form of the tool in a reversed arrangement in the Wheel rim and with only -a single direction or kind oi movement as between the Wheel and the tool and thus completing one pair of parallel tooth-surface by the singlereproduction method. This operation being repeated around the Wheel at each pitcharc interval, all the tooth-faces will be similarly completed.

in said Fig. 7, for the purpose of comparing a pair of tools, a counterpart tool T, is indicated by dotted lines in a position in which it exactly matches the aforesaid tool l, and is an exact counterpart egt thetoothform oi the Wheel. Such a counterpart tool is shown at T, Fig. 9, as employed tor malo ing the pinion-tooth g of a conjugate-curvature for correctly operating with the aforesaid tooth-form faces f3 and ,t5 of the Wheel. For this purpose, the tool T may be given the Well known "plaiier-nioveinent in the line oi the tooth-form axism (coinciding ivitli the line et' sight in F i) and at the seme time will swing in a` circle, as 8 (herein seen as an ellipse) coinciding with the geometric `pitch-surtace oi the Wheel; that is, the tool T has compoundi7 motion, comprising reciprocatory or Working movement in the line oi the instant-axis ci the wheel, While this line oit movement also revolves about the axis oi-the'ivheel. During this compound or generating operation, the pinion blank l? also revolves, (as indicated by arrows in Fig. 9) until the tool T has swung from the initial position rif" to the final position T, thereby completing both ci the faces of the pinion-tooth g by a single operation of the machine, and by a method of "compound-reproduction?7 whereby the complete master-form7 with its surfaces of uniform profile and parallel construction is reproduced in a eonjugational manner in the curved faces of the similarly parallel pinion teeth.

Figs. l() and 11 correspond to said Figs. 7 and 9, respectively ywith the exception that the tools J and T are changed places, the tool T being shown in Fig. 10 as used for making the wheel-tooth, and with the master-form faces ontwardly-converging, but with the single-reproduction, as before. Tn the companion view, Fig. l1, the counterpart tool J is shown as used for cgenerating7 the corresponding and oppositely-disposed curved faces of the pinion-teeth, with and between which the said wheel-tooth g is to directly coact. Thus in each arrangement of the master-form, the two counterpart tools by one operation of each of the tools produce four faces arranged in two pairs for direct coaction, and arranged on the lines of parallel master-forms which are identical for both the wheel and the pinion.

In making the pinions by thismethod of compGund-reproduction, the mechanism (not shown) may be operated to carry the tool, as T, Fig. 9, or J, Fig. 1l, from one said position to the other, for thereby completing one pair of the conjugate faces, as in Fig. 9 or in Fig. 11; next the pinion will be indexed through one pitch arc, and the next pair of faces be made by a reverse movement of the rolling members, to carry the tool from the said left hand position to the said right hand position in Figs. 9 and l1. Thus two pinion faces may be completed with a single tool during a. single operation of the machine.

The form or configuration of the toothsurface may be said to include the features of outline, or profile. and the relative position thereof. The character of the profile depends, of course, on the kind of reproduction, whether single, (as in the case of the wheel), or compound, (as in the case of the pinion) the position depending on the direction of the transverse convergence, whether inwardly or outwardly.

As thus applied to the wheel, each profile or side line, as f3 or f5 of the form F, gives, always by the same direct reproduction, the shape or prole, and also the position or angular relation, to one tooth-surface in each said Varrangement of the wheel construction. n the prima-ry arrangement, the said master-form, as represented in a tool (as T, Figs. 9, 16), that is coincident therewith, and by the use of the single-reproduction method, produces a pair of tooth-surfaces bounding the body of one and the same tooth, (Fig. 6a), and therefore gives to this tooth an actual sectional shape and size which is the exact counterpart of said geometric master-form. Tn the secondary arrangement, .the saine results as to outline and relative position are produced (as by `the tooth J, Fig. ll), on the two adjacent Vin practice by trial or by the aid of suitable graphic methods, having in view the extent to which in any given instance the relative Obliquity which may be desirable as between the pinion tooth-faces and the pinion-anis; in most cases an angle of Obliquity of about 10 degrees is deemed to be within practicable workingv limits. The range of variation which in practice it may be feasible to adopt, as toaXial Obliquity, I have herein designated as the co-operative relation of the pinion axis relatively to the wheel axis. Tn this connection it will, of course, be understood that the specific character or conjugate shape of the working surfaces of the pinion teeth will vary, in pairs of gears, otherwise the same, but having some particular axial Obliquity in order to nialresuch pinion surfaces properly conform to the required compouml-reproduction arrangement and configuration.

Since each wheel-tooth working-surface has uniform profiles throughout the length thereof and is of the single-reproduction configuration, when each said tooth has two such working surfaces, and these are arranged in such relation that a pair of them (either two surfaces on one tooth or two surfaces on each of two adjacent teeth), are formed in parallel, then such pair of working-surfaces is said to conform as pairs to the single-reproduction arrangement and configuration, and, conversely, the coacting pinion-tooth working-surfaces will then Vbe formed in pairs which yare said to conform as pairs tothe compound-reproduction arrangement and configuration. TWhen thus organized, each pinion-tooth is provided with a pair of working-surfaces which are individuallyT conjugate to the respective working surfaces of said wheeltooth pairs, and which also, when taken as or in pairs, conform as pairs to the compound-reproduction` arrangement and configuration. The obliquely-located wheelpair of said tooth-surfaces being of an untwisted form or construction, it follows that the mating pair of pinion-tooth-surfaces 5. nicthodlof producing a pairI of bevel gears consisting in cutting one of said gears, as the wheel, by a single-reprouuction relative movement between the blank and two relatively fixed and laterally-spaced cutting edges to thereby produce a pair of adjacent tooth surfaces with parallel surface elements, and in cutting the other of said gears, as the pinion, by a compound-reproduction relative movement as of a cone rolling upon another cone between the blank and two relatively fixed cutting edges having proiiles corresponding to said pair of adjacent tooth surfaces.

6. method of producing a pair of bevel gears consisting in cutting one of said gears, as the wheel, by a single-reproduction relative movement between the blank and two relatively fixed and laterally-spaced cutting edges to thereby produce a nair of adjacent tooth surfaces with parallel surface elements, and in cutting the other of said gears, as the pinion, by a compound-reproduction relative movement as of a cone rolling upon another cone between the blank and two relatively fixed cutting edges having profiles and fixed relation corresponding to said pair of adjacent tooth surfaces, such latter movement including a relative rolling of the blank and tool as of two pitch cone surfaces on each other.

7. A method of producing a pair of bevel gears consisting in cutting one of said gea-rs, as the wheel, by a single-reproduction relative movement between the blank and the cutting tool, the line of action of said tool relatively to the blank being skew to the axis of the blank and in cutting the other of said gears, as the pinion, by a compound-reproduction. relative movement as of a cone rolling` upon another cone between the blank and a cutting tool having a profile corresponding to the tooth face cut on the wheel.

8. A method of producing a pair of bevel gears consisting in cutting one of said gears, as the wheel., by a singl@reproduction relative movement between the blank and the cutting tool, the line of action of the tool relatively to the blank being skew to the axis of the blank and in cutting the other of said gears, as the pinion, by a compound-reproduction relative movement between the blank and a'cutting tool having a profile corresponding to the tooth face cut on the wheel, suf-h latter movement including a relative rolling of the blank and tool as of two pitch cone surfaces on each other.

9. A method of producing a bevel pinion consisting in producing a compound motion.

between a pinion blank and a tool` such inotion comprising a relative working movement longitudinally of the tooth and a generating movement involving the relative rolling of the blank and the tool on conical pitch surfaces coinciding with the geometric incarica th which said pinion is to mesh.

11. il method of producing abevel toothed pinion by compouml-reproduction consisting in giving a relative 'uf'orking movement to a pinion blank and a tool of the proi'ile forni of the tooth surface of. a gear wheel with which the said pinion is to mesh, and producing a relatively rolling movcn ent of the blank and tool on the geometric pitch cone surfaces of the blank and of said bevel gear wheel.

12. A method of cutting a bevel pinion consisting in producing a rectilinear relative cutting movement between a pinion blank and a cutter of the profile forni of the tooth surface of a gear wheel with which the pinion is to mesh, and producing a relative profile generating movement between the blank and cutter corresponding to the relative movement of the finished pinion and a mating bevel gear when the pitch cone of one is rolling upon the pitch cone of the other.

i method of producing a pair of bevel 'fears consisting in cutting one of said gears,

wheel, by a single-reproduction rectirelative movement between the wheel and two cutting edges engaging diftooth-Surfaces of said blank to thereby produce a pair of adjacent tooth surfaces of uniform profile and with parallel surface elements constituting a master-form, and in cutting the other of said gears, as the pinion, by a compound-reproduction relative movement as of a cone rolling upon another cone between the blank andcutting edges corresponding to such master-form.

A method of producing abevel toothed pinionby compmind-reproduction consisting in giving a pinion blank and tool a rectilinear relative working movement longitudina-lly of the tooth and producing a relatively rolling movement of the blank and tool on the geometric pitch cone surfaces of the blank and of the bevel gear wheel with which said pinion is to mesh.

15. A method of cutting a pinion tooth surface which consists in producing a relative cutting movement, in a direction skew to the axis of the pinion blank and oblique with reference to a line parallel to said axis, between such pinion blank and a cutter of the profile form of the gear wheel with which the pinion is to mesh, and producing` a relative profile generating movement etween the said blank and the cutter corresponding to the relative movement of the finished pinion and a mating gear wheel when one is rolling upon the other. y

16. A method of cutting a pinion tooth surface which consists in producing a relative cutting movement, longitudinally of the said surface and skew to the axis of the pinion blank and obliquely with reference to a line parallel to said axis, between such pinion blank and a cutter of the profile form of the gear wheel with which the pinion is to mesh, and producing a relative profile generating movement between said blank and cutter corresponding to the relative movement of the finished pinion and mating gear wheel when one is rolling upon the other.

17. A methodof cutting a tooth surface on a pinion blank which consists in producing a relative cutting movement, in a straight line skew to the axis of the pinion blank and oblique with reference to a line parallel to said axis, between such pinion blank and a cutter of the profile form of the gear wheel with which the pinion is to mesh, and producing a relative profile generating movement between said blank and cutter corresponding to the relative movement of the finished pinion and a mating gear wheel when one is rolling upon the other.

18. A method of cutting on a pinion blank a pair of tooth surfaces containing pairs of parallel longitudinal line elements, which consists in producing a relative cutting movement, in a direction oblique with reference to a line parallel to the axis of said blank, between such pinion blank and two cutting edges which are fixed relatively to each other and spaced or offset so as to engage different tooth-surfaces of said blank, and producing a relative profile generating movement between said blank and cutter corresponding to the relative movement of the finished pinion and a mating gear wheel when one is rolling upon the other, to thereby produce a pair of adjacent tooth surfaces each having longitudinal` line elements of such character that to each line element of one of said surfaces corresponds a parallel longitudinal line element on the other surface of the same pair.

19. A method of cutting on a pinion blank a pair of tooth surfaces each of which contains longitudinal straight line elements of such character that each straight line element of one of said surfaces corresponds to a parallel straight longitudinal line element on the other surface of the same pair, which consists in producing a relative rectilinear cutting movement between said blank and two relatively fixed cutting edges located laterally of each other with reference to the direction of such movement, which direction is oblique to a line parallel to the axis of the pinion blank, and producing a duction relative movement between the wheel A blank and two cutting edges arranged on opposite sides of a'master-form axis parallel to the direction of said relative cutting movement, to thereby produce a pair of adjacent tooth surfaces of uniform profile and with longitudinal line elements parallel to said master-form axis, and in cutting the other gear, as the pinion, by a compound-reproduction relative movement between the pinion blank and cutting edges corresponding to said master-form.

2l. A method of producing a pair of mating gears, which consists in cutting one of said gears, as the wheel, by a single-reproduction relative movement, obliquely with reference to a line parallel to the axis of the wheel blank, between such wheel blank and two cutting edges arranged on opposite sides of a master-form axis parallel to the direction of said relative cutting movement, to thereby produce a pair of adjacent tooth surfaces of uniform profile and with longitudinal line elements parallel to said masterform axis, and in cutting the other gear, as the pinion, by a compound-reproduction relative movement between the pinion blank and cutting edges corresponding to said master-form.

22. A method of producing a pair of mating gears, which consists in cutting one of said gears, as the wheel, by a relative rectilinear single-reproduction movement, obliquely with reference to a line parallel to the axis of the wheel blank, between such wheel blank and two cutting edges arranged on opposite sides of a straight master-ferm axis parallel to the direction of said rectilinear relative cutting movement, to thereby produce a pair of adjacent tooth surfaces of uniform profile throughout their length and Y with straight longitudinal line elements parallel to said straight master-form axis, and in cutting the other gear, as the pinion, by a compound-reproduction relative movement between the pinion blank and cutting edges corresponding to said master-form.

23. A method of producing a pair of mating gears, which consists in cutting one of said gears, as the wheel, by a singlereproduction relative movement between the wheel blank and a cutter, in a direction oblique with reference to a line parallel to the axis of said blank, and in cutting the other gear, as the pinion, by a compound-reproduction relative movement betweenthe pinion blank and a cutter ot a profile-form which is the counterpart ot the wheel-cutter.

24. A method of producing a pair of meshing gears, which consists in cutting onerof said gears, as the wheel, by a single-reproduction rectilinear relative movement lbetween thewheel blank and a cutter, in a direction oblique with reference to a lineparallel to the axis of saidblanlr, and in cutting` the other gear, asrthe pinion, by a compoundreproductionrelative movement between the pinion blank anda cutter of a profile-form which is a counterpart ofthe wheel-cutter.

method of producing a pair of inating gears, which consists in making oneoIn them, as the wheel, with untwisted tooth surfaces ot single-reproduction character, and the other gear, as the pinion, with longitudinally-twisted tooth-surfaces of compoundreproduction configuration, whereby the longitudinal twist of the working tooth-surfaces will be confined to one of said gears, as the pinion, the other gear, as the wheel, being tree from such longitudinal twist.

ln testimony whereof l atHX my signature.

HARVEY D. WILLIAMS. 

